Globally optimal superconducting magnets part I: minimum stored energy (MSE) current density map

An optimal current density map is crucial in magnet design to provide the initial values within search spaces in an optimization process for determining the final coil arrangement of the magnet. A strategy for obtaining globally optimal current density maps for the purpose of designing magnets with coaxial cylindrical coils in which the stored energy is minimized within a constrained domain is outlined. The current density maps obtained utilising the proposed method suggests that peak current densities occur around the perimeter of the magnet domain, where the adjacent peaks have alternating current directions for the most compact designs. As the dimensions of the domain are increased, the current density maps yield traditional magnet designs of positive current alone. These unique current density maps are obtained by minimizing the stored magnetic energy cost function and therefore suggest magnet coil designs of minimal system energy. Current density maps are provided for a number of different domain arrangements to illustrate the flexibility of the method and the quality of the achievable designs.